It just happens that certain keys have common characteristics both on woodwinds and strings. Playing in A, you will use three of the four strings on a violin open, so that'll give you a brighter effect. On a flute, the only crossfingered note in the A scale is G#, so again you get a bright sound. In E flat, the tonic, fourth and fifth are muted by stopping or crossfingering for both instruments. Much the same goes for the oboe.

On a harp, it's the other way round. Harps are usually made in flat keys, with semitonal sharpenings, and you get a beefier sound with unsharpened strings. There was a lot of music in flat keys published in Scotland during the years when the harp was fashionable - roughly 1790-1830 - and fiddlers tend to forget that the title pages usually specify the instruments as "FOR THE HARP, PIANOFORTE, Violin, German Flute, Violoncello..." with the lettering getting steadily smaller down the list. Selling to harpists obviously made commercial sense and the music reflected that. So for that stuff, the key associations had to work differently insofar as they featured at all.

This has nothing to do with temperament.